COOK bacon in nonstick skillet until crisp; remove from skillet, reserving 1 tsp. drippings in skillet. Drain bacon on paper towels.
ADD egg to drippings in skillet; cook on medium heat 3 to 4 min. or until white is set and yolk is cooked to desired doneness, turning after 2 min. Remove from heat. Break bacon slices in half. Top egg with 2 bacon pieces and cheese.
SPREAD cut sides of bread with mayo; fill with lettuce, tomatoes, remaining bacon pieces and egg.